Weighted cscK metrics on Kähler varieties
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917277147856896 |
|---|---|
| author | Pan, Chung-Ming Tô, Tat Dat |
| author_facet | Pan, Chung-Ming Tô, Tat Dat |
| contents | We study the weighted constant scalar curvature Kähler equations on mildly singular Kähler varieties. Assuming the existence of a suitable resolution of singularities, we establish the existence of singular weighted cscK metrics when the weighted Mabuchi functional is coercive for an extremal weight. This extends the works of Chen-Cheng and He to the singular weighted setting. Moreover, we provide a method for constructing examples of singular cscK metrics inspired by the work of Arezzo-Pacard. In contrast to the usual gluing techniques, our approach does not require a precise understanding about of the metric behavior near the singular locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted cscK metrics on Kähler varieties Pan, Chung-Ming Tô, Tat Dat Differential Geometry Analysis of PDEs Complex Variables We study the weighted constant scalar curvature Kähler equations on mildly singular Kähler varieties. Assuming the existence of a suitable resolution of singularities, we establish the existence of singular weighted cscK metrics when the weighted Mabuchi functional is coercive for an extremal weight. This extends the works of Chen-Cheng and He to the singular weighted setting. Moreover, we provide a method for constructing examples of singular cscK metrics inspired by the work of Arezzo-Pacard. In contrast to the usual gluing techniques, our approach does not require a precise understanding about of the metric behavior near the singular locus. |
| title | Weighted cscK metrics on Kähler varieties |
| topic | Differential Geometry Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2412.07968 |